Task - Illustrative Mathematics
... hypothesis and |AP| = |AP|. By the Pythagorean theorem, |BP| = |CP|, and so by SSS △BPA is congruent to △CPA. Hence m(∠B) = m(∠C). One alternate proof, building on the picture from Courtney's solution, uses trigonometric ratios. Using the picture above, we have sin ∠B = |AP| and ...
... hypothesis and |AP| = |AP|. By the Pythagorean theorem, |BP| = |CP|, and so by SSS △BPA is congruent to △CPA. Hence m(∠B) = m(∠C). One alternate proof, building on the picture from Courtney's solution, uses trigonometric ratios. Using the picture above, we have sin ∠B = |AP| and ...
Lesson Plan: Criteria for Triangle Congruence
... Discuss which stations led to multiple triangles and which stations always produced congruent triangles. (Look for evidence of MP3.) 4. Ask students, “Based on what we discovered today what criteria should allow us to conclude that two triangles are congruent and what criteria would be insufficient ...
... Discuss which stations led to multiple triangles and which stations always produced congruent triangles. (Look for evidence of MP3.) 4. Ask students, “Based on what we discovered today what criteria should allow us to conclude that two triangles are congruent and what criteria would be insufficient ...
Triangle congruence and similarity
... reflection in DE. In the first case, C’=F and we’re done. Otherwise, to superpose ∆A’B’C’ onto ∆DEF, reflect it across DE. Since reflections preserve distance and angle measure, C” = F. Theorem: (ASA congruence) If two angles of one triangle have equal measures to two angles of another, and if the ...
... reflection in DE. In the first case, C’=F and we’re done. Otherwise, to superpose ∆A’B’C’ onto ∆DEF, reflect it across DE. Since reflections preserve distance and angle measure, C” = F. Theorem: (ASA congruence) If two angles of one triangle have equal measures to two angles of another, and if the ...